Molar mass colligative properties

The molecular weight of a substance is, for a large number of calculations, far more convenient than unit mass. This depends on the fact that a large number of properties are independent of the nature of the substance, and depend only on the number of molecular weights present ( molar, or colligative, properties) (cf. Chap. XI. on Solutions ). 

The experimental measurement of these averages has largely been performed on polymers in solution (Hunt and James, 1999). Since M depends on the measurement of the number of polymer chains present in a given mass, colligative properties such as vapour-pressure depression AP (measured by vapour-phase osmometry) and osmotic pressure (measured by membrane osmometry) relative to the pure solvent, can in principle provide the molar mass through an equation of the form... 

Determination of Molar Masses from Colligative Properties... 

Colligative properties, particularly freezing point depression, can be used to determine molar masses of a wide variety of nonelectrolytes. The approach used is illustrated in Example 10.9. 

A laboratory experiment on colligative properties directs students to determine the molar mass of an unknown solid. Each student receives 1.00 g of solute, 225 mL of solvent and information that may be pertinent to the unknown. 

Molar masses can also be determined using other colligative properties. Osmotic pressure measurements are often used, particularly for solutes of high molar mass, where the concentration is likely to be quite low. The advantage of using osmotic pressure is that the effect is relatively large. Consider, for example, a 0.0010 M aqueous solution, for which... 

Use colligative properties to determine molar mass of a solute. 

HOWTO USE COLLIGATIVE PROPERTIES TO DETERMINE MOLAR MASS... 

The lowering of freezing point and the generation of osmotic pressure both depend on the total concentration of solute particles. Therefore, by using the colligative property to determine the amount of solute present, and knowing its mass, we can infer its molar mass. 

Colligative properties can be sources of insight into not only the properties of solutions, but also the properties of the solute. For example, acetic acid, CH.COOH, behaves differently in two different solvents, (a) The freezing point of a 5.00% by mass aqueous acetic acid solution is — l.72°C. What is the molar mass of the solute Explain any discrepancy between the experimental and the expected molar mass, (b) The freezing-point depression associated with a 5.00% by mass solution of acetic acid in benzene is 2.32°C. Whar is the experimental molar mass of the solute in benzene What can you conclude about the nature of acetic acid in benzene ... 

For practical purposes, the colligative property that is most useful for measuring relative molar masses of polymers is osmotic pressure. As Table 6.2 shows, all other properties take such small values that their measurement is impractical. 

Colligative properties measure average relative molar masses, M, and in the case of osmotic pressure, II, the important relationship is ... 

Table 6.2 Colligative properties of a solution of polymer of molar mass 20 000 at a concentration o/O.Ol g (from F. W. Billmeyer, Textbook of Polymer Science , John Wiley Sons, New York, 1962)...

Vapour pressure osmometry is the second experimental technique based on colligative properties with importance for molar mass determination. The vapour pressure of the solvent above a (polymer) solution is determined by the requirement that the chemical potential of the solvent in the vapour and in the liquid phase must be identical. For ideal solutions the change of the vapour pressure p of the solvent due to the presence of the solute with molar volume V/1 is given by... 

The osmotic pressure is a colligative property and mathematically can be represented as 71 = (nRTIV) i, where It is the osmotic pressure in atmospheres n is the number of moles of solute R is the ideal gas constant 0.0821 L atm/Kmol T is the Kelvin temperature Vis the volume of the solution and i is the van t Hoff factor. Measurements of the osmotic pressure can be used to calculate the molar mass of a solute. This is especially useful in determining the molar mass of large molecules such as proteins. 

The colligative properties, described in Section 3.4.1 to Section 3.4.3, have been used to determine the molar mass of unknown chemical compounds. Pharmaceutical scientists and pharmacists may apply this concept in the preparation of isotonic (meaning of equal tone) solution dosage forms. These solution dosage forms can be applied to sensitive and delicate organs such as the eye, nose, or ear or directly injected into the body (i.e., blood vessels, muscles, lesions, etc.). They should have, when administered, the same osmotic pressure as body fluids. Otherwise, transport of body fluids inside and outside the cell tissues will occur, causing discomfort and damage to the tissue. Osmolarity of body fluids is approximately 0.307 osmol/L or 307 mosmol/L. 

One of the laboratory requirements for the course, and also the topic of former test questions, is the determination of the molar mass of a substance from the freezing-point depression. Actually, any of the colligative properties can be used to determine the molar mass, but the only one that you are required to know is the freezing-point depression method. It is easier to illustrate the technique within the framework of a problem, so the discussion of this process will be done within a sample problem. 

Rudin s aim was to predict the size of dissolved polymer molecules and the colligative properties of polymer solutions (hydrodynamic volume, second virial coefficient, interaction parameter, osmotic pressure, etc) from viscometric data (average molar mass, intrinsic viscosity, etc.). 

In the 1920s, it was not feasible to accurately measure the molecu-f lar weight of natural or synthetic polymers. Classical methods 1 of molecular weight determina-V tion, those based upon colligative x properties, elevation of boiling point, depression of freezing point and lowering of vapor pressure, worked very well for low-molar-mass compounds, but were essentially useless for macromolecules. Modern instrumental methods that... 

Osmotic pressure can be used to characterize solutions and determine molar masses just as the other colligative properties can however, osmotic pressure is particularly useful because a small concentration of solute produces a relatively large osmotic pressure. 

Calculate the molar mass of a nonvolatile solute from the changes it causes in the colligative properties (vapor-pressure lowering, boiling-point elevation, freezing-point lowering, or osmotic pressure) of its dilute solution (Section 11.5, Problems 41-56). 

There are several ways to measure the concentration of a solution, five of which you should know for the MCAT molarity (M), molality ), mole fraction (%), mass percentage and parts per million (ppm). Molarity is the moles of the compound divided by the volume of the solution. Molarity generally has units of mol/L. Molality is moles of solute divided by kilograms of solvent. Molality generally has units of mol/kg and is usually used in formulae for colligative properties. The mole fraction is the moles of a compound divided by the total moles of all species in solution. Since it is a ratio, mole fraction has no units. Mass percentage is 100 times the ratio of the mass of the solute to the total mass of the solution. Parts per million is 106 times the ratio of the mass of the solute to the total mass of the solution. 

As we have emphasized, colligative properties depend on the number of solute particles in a given mass of solvent. A 0.100 molal aqueous solution of a covalent compound that does not ionize gives a freezing point depression of 0.186°C. If dissociation were complete, 0.100 m KBr would have an ejfective molality of 0.200 m (i.e., 0.100 m K+ + 0.100 m Br ). So we might predict that a 0.100 molal solution of this 1 1 strong electrolyte would have a freezing point depression of 2 X 0.186°C, or 0.372°C. In fact, the observed depression is only 0.349°C. This value for ATf is about 6% less than we would expect for an effective molarity of 0.200 m. 

The colligative properties are of importance by themselves, but they can also be used to determine the molar mass of a solute, since they all depend on the molar concentration and since the mass concentration generally is known. To this end, the determination of the freezing point often is most convenient. Because of nonideality, determinations should be made at several concentrations and the results extrapolated to zero. For determination of the molar mass of macromolecules, osmotic pressure measurement is to be preferred, since membranes exist that are not permeable for macromolecules, while they are for small-molecule solutes, and even small quantities of the latter have a relatively large effect on the colligative properties. Actually, a difference in osmotic pressure is thus determined, the difference being due to the macromolecules only. 

In Chapter 12 you learned about the colligative properties of solutions. Which of the colligative properties is suitable for determining the molar mass of a polymer Why ... 

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